Final answer:
The probability of choosing a red marble without replacement and then choosing a red marble again is 5/33.
Step-by-step explanation:
To find the probability of choosing a red marble without replacement and then choosing a red marble again, we need to calculate the probability of each event separately and multiply them together.
First, there are 5 red marbles out of a total of 2 purple marbles, 2 blue marbles, 3 green marbles, and 5 red marbles, so the probability of choosing a red marble without replacement is 5/12.
Next, after taking out one red marble, the total number of marbles decreases to 11, and now there are 4 red marbles left. So the probability of choosing a red marble again is 4/11.
To find the probability of both events occurring, we multiply the probabilities: (5/12) * (4/11) = 20/132 = 5/33.